原子核反応と 環境、摩擦、量子デコヒーレンス Role of internal degrees of freedom in low-energy nuclear reactions Kouichi Hagino (Tohoku University) 1. Introduction: Environmental Degrees of Freedom Introduction: Environmental Degrees of Freedom 1. 2. Mott Scattering and Quantum Decoherence 2. Mott Scattering and Quantum Decoherence 3. Application of RMT to subbarrier fusion 3. Application of RMT to subbarrier fusion and scattering (Introduction) and scattering (Introduction) 4. Summary Summary 4.
Deep subbarrier 核融合と decoherence にまつわる最近の論文 C.C. (coherent) うまくいかない C.C. が coherent だからに違いない
Introduction: Quantum Decoherence とは ? Coherent superposition interference In macroscopic systems, no superposition: Quantum decoherence theory Couplings to environment Quantum to classical transition
Deep subbarrier 核融合と decoherence にまつわる最近の論文 彼らの解釈は正しいのか ? 核融合反応断面積の式はもともと incoherent sum 彼らの議論は conjecture に過ぎない (decoherence がないとした 場合との比較をしていない）
Deep subbarrier 核融合と decoherence にまつわる最近の論文 彼らの解釈は正しいのか ? 核融合反応断面積の式はもともと incoherent sum 彼らの議論は conjecture に過ぎない (decoherence がないとした 場合との比較をしていない） • 「デコヒーレンス」を「複雑な内部自由度との結合の効果」と読み 替えると正しいかもしれない（同意してくれる人は多い） • 核融合ではなく、他の反応プロセスであればデコヒーレンスが見える かもしれない ?
原子核反応と 環境、摩擦、量子デコヒーレンス Role of internal degrees of freedom in low-energy nuclear reactions Kouichi Hagino (Tohoku University) 1. Introduction: Environmental Degrees of Freedom Introduction: Environmental Degrees of Freedom 1. 2. Mott Scattering and Quantum Decoherence 2. Mott Scattering and Quantum Decoherence 3. Application of RMT to subbarrier fusion 3. Application of RMT to subbarrier fusion and scattering (Introduction) and scattering (Introduction) 4. Summary Summary 4.
Introduction atomic nuclei: microscopic systems little effect from external environment E * These states are excited during nuclear reactions in a complicated way. nuclear intrinsic d.o.f. act as environment for nuclear reaction processes “ intrinsic environment” nuclear spectrum
How have “internal excitations” been treated in nuclear physcs ? 1. Optical potential elimination of “environmental” d.o.f. effective potential Feschbach formalism Phenomenological potential absorption of flux 2. Coupled-channels method (Close coupling method) Coupling between rel. entrance 0 + 0 + and intrinsic motions channel 0 + 0 + excited 2 + 0 + channel treat a few (collective) excited 4 + 0 + states explicitly channel
3. Classical treatment e.g., Langevin calculations for superheavy elements Courtesy Y. Aritomo (JAEA)
nuclear excitations E * “ intrinsic environment” In this talk: Mott scattering and quantum decoherence Role of s.p. excitations in quantum tunneling （次の遊佐君のトークの背景） c.f. Random Matrix Model nuclear spectrum
Mott scattering and quantum decoherence Kouichi Hagino (Tohoku University) M. Dasgupta (ANU) D.J. Hinde (ANU) R. McKenzie (Queensland) C. Simenel (ANU) M. Evers (ANU) on-going work
Mott Oscillation scattering of two identical particles cf. V b ~ 10.3 MeV “Quantum Physics”, S. Gasiorowicz expt: D.A. Bromley et al., Phys. Rev. 123 (‘61)878
Mott Oscillation cf. V b ~ 10.3 MeV “Quantum Physics”, S. Gasiorowicz expt: D.A. Bromley et al., Phys. Rev. 123 (‘61)878 2 つの経路の干渉 デコヒーレンスが起きて干渉が消える ことは原子核反応であるのか ? （ cf. 2 つの経路で最近接距離は異なる）
Comparison between 16 O+ 16 O and 18 O+ 18 O 16 O, 18 O: I g.s.) = 0 + (both are bosons) V b ~ 10.3 MeV E cm ~ 2.5 V b 18 O+ 18 O : much less pronounced interference pattern 18 O = 16 O (double closed shell) + 2n stronger coupling to environment manifestation of environmental decoherence?
Optical potential model calculation The data can be fitted with an However, the same opt. pot. opt. pot. model calculation. does not fit 18 O+ 18 O W = 0.4 + 0.1 E cm (MeV) need to increase W by a factor R.H. Siemssen et al., PRL19 (‘67) 369 of 3.5
The origin of stronger absorption? (MeV) 3 - 6.13 0 + 5.10 3 - 3.92 0 + ,2 + ,4 + 2 + 1.98 0 + 0 + 16 O 18 O Coupling to low-lying 2 + state: insufficient to damp the oscillation role of single-particle (non-collective) excitations
56 levels 18 O Spectra up to E* = 13 MeV 20 levels 16 O
C. Von Charzewski, V. Hnizdo, and F. Haas and Y. Abe, PRL46(‘81)1667 C. Toepffer, NPA307(‘78)309 The number of open channels N(E*,R): the density of accessible 1p1h states (TCSM) 18 O+ 18 O 16 O+ 16 O
Mechanisms of the oscillatory structure The unsymmtrized cross sections already show strong oscillations interference due to: symmetrization of wave function ( ~ 90 deg.) + another mechanism
near side-far side interference R.C. Fuller, PRC12(‘75)1561 N. Rowley and C. Marty, NPA266(‘76)494 M.S. Hussein and K.W. McVoy, Prog. in Part. and Nucl. Phys. 12 (‘84)103
The far-side component is largely damped in 18 O+ 18 O due to the strong absorption. less oscillatory pattern
The distance of closest apporach: different between F and N F and N are distinguishable (in principle) by looking at how the nuclei get excited “which-way information”
analogy to the double slit problem M.S. Hussein and K.W. McVoy, J. Al-Khalili, “Quantum” Prog. in Part. and Nucl. Phys. 12 (‘84)103
J. Al-Khalili, “Quantum”
close analogy to environmental decoherence? P. Sonnentag and F. Hasselbach, PRL98(‘07)200402
Subbarrier fusion reactions with dissipative couplings Kouichi Hagino (Tohoku University) Shusaku Yusa (Tohoku University) Neil Rowley (IPN Orsay) S. Yusa, K.H., and N. Rowley, PRC82(‘10)024606
Introduction Subbarrier enhancement of fusion cross section channel coupling effects Coupling of the relative motion to collective excitations in the colliding nuclei 16 O 154 Sm
Coupled-channels framework Coupling between rel. entrance 0 + 0 + and intrinsic motions channel 0 + 0 + excited 2 + 0 + channel excited 4 + 0 + channel Quantum theory which incorporates excitations in the colliding nuclei a few collective states (vibration and rotation) which couple strongly to the ground state + transfer channel
IS Octupole response of 48 Ca (Skyrme HF + RPA calculation: SLy4) collective state: strong coupling single-particle (non-collective) state weak, but many
Coupled-channels framework Coupling between rel. entrance 0 + 0 + and intrinsic motions channel 0 + 0 + excited 2 + 0 + channel excited 4 + 0 + channel Quantum theory which incorporates excitations in the colliding nuclei a few collective states (vibration and rotation) which couple strongly to the ground state + transfer channel several codes in the market: ECIS, FRESCO, CCFULL…… has been successful in describing heavy-ion reactions However, many recent challenges in C.C. calculations!
surface diffuseness anomaly Scattering processes: Double folding potential Woods-Saxon (a ~ 0.63 fm) successful A. Mukherjee, D.J. Hinde, M. Dasgupta, K.H., et al., PRC75(’07)044608 Fusion process: not successful a ~ 1.0 fm required (if WS)
Deep subbarrier fusion data C.L. Jiang et al., PRL93(’04)012701 “steep fall-off of fusion cross section” K. H., N. Rowley, and M. Dasgupta, PRC67(’03)054603 M.Dasgupta et al., PRL99(’07)192701
energy dependence of surface diffuseness parameter M. Dasgupta et al., PRL99(’07)192701 potential inversion with deep subbarrier data K.H. and Y. Watanabe, PRC76 (’07) 021601(R)
energy dependence of surface diffuseness parameter potential inversion with deep subbarrier data K.H. and Y. Watanabe, PRC76 (’07) 021601(R) dynamical effects not included in C.C. calculation? energy and angular momentum dissipation? weak channels?
A hint: comparison between 20 Ne+ 90 Zr and 20 Ne+ 92 Zr (E eff = 50 MeV) C.C. results are almost the same between the two systems Yet, quite different barrier distribution and Q-value distribution E. Piasecki et al., single-particle excitations?? PRC80 (‘09) 054613
role of these s.p. levels in barrier distribution and Q-value distribution? 遊佐君のトーク 90 Zr (Z=40 sub-shell closure, N=50 shell closure) 92 Zr = 90 Zr + 2n cf. 18 O = 16 O + 2n
Summary Single-particle (non-collective) excitations in H.I. reactions Non-collective excitations in isolated nuclei 18 O + 18 O 20 Ne + 92 Zr after touching: molecular excitations Random matrix Deep subbarrier fusion model
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